SOLUTION: w={(x,y): x=3y=0} , v=R square is w a subspace of v?

Question 940080: w={(x,y): x=3y=0} , v=R square
is w a subspace of v?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Remember the definition of a subspace.
Contains the zero vector of R2.
If U and V are in w, U+V is in w.
For each scalar a, if U is in w, aU is in w.
.
.
.
w fails the first criteria, since w is a single point (3,0), the zero vector is not in w.
So no w is not a subspace of R2.

RELATED QUESTIONS
w={(x,y): x=3y=0} , v=R square is w a subspace of... (answered by Fombitz)

Let V=R^3 and let W={(x, y, z) ∈ R^3| x=3y} Is W a subspace of V? If it is, find (answered by ikleyn)

Consider the following subspace of R^3: W={(x,y,z)belong to R^3|2x+2y+z=0, (answered by Fombitz)

let V = F be the vector space of all real-valued functions and Let W = {f ∈ F :... (answered by robertb)

4.let U= {q,r,s,t,u,v,w,x,y,z}; A= {q,s,u,w,y};and C={v,w,x,y,z,}; list the members of... (answered by Edwin McCravy)

Let a be a fixed vector in R^3, and define W to be the subset of R^3 given by W={x:... (answered by khwang)

What is a subspace ? How do you prove that it is a subspace ? I know that it is a... (answered by robertb)

Question 1 please help me with this question. If the universal set U=... (answered by MathLover1)

how do i prove W^(perpendicular sign) is a subspace of... (answered by venugopalramana)